Families of Hillsborough disaster victims have accused the head of Scotland Yard of making misleading statements about an inquiry into the tragedy and have called for an investigation. They say that Sir Bernard Hogan-Howe, the Metropolitan police commissioner, failed to tell the truth last year when he claimed to have made a statement to Lord Justice Taylor's 1989 inquiry into how 96 football fans died.

The families want the Independent Police Complaints Commission to investigate his account and why he appears never to have made an official statement to the inquiry despite having been an inspector in South Yorkshire police at the time of the disaster. They want the IPCC to look into his actions on the day.

Their demands come amid a continuing IPCC investigation into alleged police misconduct during and in the aftermath of Britain's worst sporting disaster.

Hogan-Howe said he had been confused when he said he made a statement to the Taylor inquiry. In fact, the account he referred to is a brief, six-line note of a telephone conversation in May 1990, when Taylor's inquiry was over. He said he wants the IPCC to investigate the account he gave after Hillsborough as part of its current investigation.

The investigation has confirmed that it will examine Hogan-Howe's actions on the day. He was the officer in charge at a Sheffield boys' club in which friends and relatives waited for news. The investigation has confirmed that it will examine Hogan-Howe's actions on the day of the disaster. At 7.20pm a senior police officer, his identity still unknown, read out a list of people confirmed to be "safe and well". The list included Adam Spearritt – who was 14 when he died at Hillsborough. Friends who had gone to the match with Adam and his father, Eddie, telephoned Jan Spearritt, Adam's mother, to reassure her that her son was alive. She says that incorrect identification added to their anguish. The family never complained about that mistake, but have always been particularly unhappy that South Yorkshire police, despite repeated requests, refused to explain how it happened. Sir Norman Bettison, then a chief inspector in South Yorkshire police, was involved in organising the waiting area in the boys club and compiling the missing persons list. Both he and Hogan-Howe later became chief constables of Merseyside police, Bettison from 1998-2005; Hogan-Howe from 2005-2009.

Following last September's Hillsborough Independent Panel report into the disaster, Hogan-Howe was asked about his actions on the day. He replied that he "provided statements to the Taylor report about his role following the tragedy".

Those statements did not, however, appear in the archive of official documents published by the panel. One document, dated 18 May 1990, noted that an Inspector Sawers of West Midlands police (the force appointed to investigate the disaster) had contacted Hogan-Howe, to "ascertain whether Insp [sic] Hogan-Howe, who was at the boys' club, Hammerton Road, arranging the policing, has anything relevant to add to the inquiry".

Hogan-Howe said Sawers had telephoned him after he had given "investigators" his account. "When asked later [by Sawers] if I wanted to add to [my] account, I said I did not," he said.

The Metropolitan police then forwarded the document Hogan-Howe had been referring to as the account he gave to investigators of his role in the disaster. It is not, in fact, a statement provided to the Taylor inquiry; it is a very brief note of a telephone conversation with PC Kenneth Greenway, of the South Yorkshire police. Greenway's six-line account of his conversation with Hogan-Howe includes only this about the boys' club: "Going to the Hillsborough boys' club and had dealing with social services, relatives etc. I finished at 3.30am on Sun 16/04/89."

That is the note Hogan-Howe has described as his "account of my role" given to "investigators" and as "statements to the Taylor report".

It is dated 23 May 1990, long after Taylor had completed his report. It was also five days after Hogan-Howe was contacted by Sawers to see if he had "anything relevant to add to the inquiry". Sawers was not calling him "later," to "add to this account", as Hogan-Howe said. In fact when Sawers called him, Hogan-Howe had not made any statement, and he apparently declined then to make "a comprehensive statement".

Paul Spearritt, Adam's younger brother, said he was shocked by Hogan-Howe's apparently misleading statements about the accounts he had given of his role at Hillsborough, and called on the IPCC to conduct a full investigation.

"In all these years we have never had any explanation as to why Adam was in the list as 'alive and well,' no identification of which police officer read it out, no apology from that officer – no admission that it even happened," he said.

Hogan-Howe explained his incorrect statements about the accounts he gave of his actions at Hillsborough, saying his "confusion" was due to recollecting events of more than 20 years ago.

Of the incorrect naming of Adam Spearritt as "alive and well" in the boys club the night of the disaster, Hogan-Howe said: "I only became aware of the complaint or criticism regarding the reading out of a list by an officer earlier this year. If I had been aware, I would have been more than eager to provide what information I could."

Margaret Aspinall, chair of the Hillsborough Family Support Group, to which the Spearritt family is affiliated, said she is "furious" that Hogan-Howe has blamed "confusion" for his misleading statements about the accounts he gave of Hillsborough: "It is incredible that the top police officer in the country has not told the truth about the account he gave when 96 people lost their lives, and it is difficult to believe he was confused. It is also astonishing he has never made a detailed statement about what he did as the senior officer in charge of bereaved people at the boys' club. I am calling on the IPCC to fully investigate."